Exact ground and excited states of frustrated antiferromagnets on the CaV_4O_9 lattice

TL;DR

This paper constructs an exact spin-1/2 model on the CaV_4O_9 lattice, demonstrating the precise ground and excited states, including a plaquette resonating-valence-bond state, relevant for understanding its spin-gap behavior.

Contribution

It introduces a specific model where the PRVB state is exactly solvable as the ground state, and also determines the first excited state analytically.

Findings

PRVB state is the exact ground state in a certain parameter regime

First excited state can be exactly calculated within this regime

Dimer state is the exact ground state in a different parameter regime

Abstract

The experimental observation of a spin-gap in the antiferromagnetic spin-1/2 compound $CaV_4O_9$ has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.